Given \(\lim\limits_{\text x \to 2}\cfrac{\sqrt{\text x^2+1}-\sqrt5}{\text x - 2}\)
To find: the limit of the given equation when x tends to 2
Substituting x as 2, we get an indeterminant form of
Rationalizing the given equation
Formula: (a + b) (a - b) = a2 - b2
Now we can see that the indeterminant form is removed, so substituting x as 2
We get \(\lim\limits_{\text x \to 2}\cfrac{\sqrt{\text x^2+1}-\sqrt5}{\text x - 2}\) = \(\cfrac{2+2}{2\sqrt5}=\cfrac{2}{\sqrt5}\)